Below is a collected list of low(ish) rank Verlinde categories. Click on the names for more information, including the fusion rules, Frobenius-Perron dimensions of the simple objects, and modular data. Please see the conventions page for how to use the site. The goal is to be a kind of landing page for quick references to these categories for researchers and anyone interested.

For questions and/or suggestions, please email abaxi [AT] tamu [DOT] edu or open a GitHub issue. Replace the bracketed terms with the obvious replacements.

Category Rank $D^2$ Cartan Type Level
\(\operatorname{SU}(2)_{1}\) 2 2.000 \( A_{1} \) 1
\(\operatorname{E}_{8}(2)\) 3 4.000 \( E_{8} \) 2
\(\operatorname{SO}(11)_{1}\) 3 4.000 \( B_{5} \) 1
\(\operatorname{SO}(13)_{1}\) 3 4.000 \( B_{6} \) 1
\(\operatorname{SO}(15)_{1}\) 3 4.000 \( B_{7} \) 1
\(\operatorname{SO}(17)_{1}\) 3 4.000 \( B_{8} \) 1
\(\operatorname{SO}(19)_{1}\) 3 4.000 \( B_{9} \) 1
\(\operatorname{SO}(21)_{1}\) 3 4.000 \( B_{10} \) 1
\(\operatorname{SO}(23)_{1}\) 3 4.000 \( B_{11} \) 1
\(\operatorname{SO}(25)_{1}\) 3 4.000 \( B_{12} \) 1
\(\operatorname{SO}(27)_{1}\) 3 4.000 \( B_{13} \) 1
\(\operatorname{SO}(29)_{1}\) 3 4.000 \( B_{14} \) 1
\(\operatorname{SO}(31)_{1}\) 3 4.000 \( B_{15} \) 1
\(\operatorname{SO}(33)_{1}\) 3 4.000 \( B_{16} \) 1
\(\operatorname{SO}(35)_{1}\) 3 4.000 \( B_{17} \) 1
\(\operatorname{SO}(37)_{1}\) 3 4.000 \( B_{18} \) 1
\(\operatorname{SO}(5)_{1}\) 3 4.000 \( B_{2} \) 1
\(\operatorname{SO}(7)_{1}\) 3 4.000 \( B_{3} \) 1
\(\operatorname{SO}(9)_{1}\) 3 4.000 \( B_{4} \) 1
\(\operatorname{SU}(2)_{2}\) 3 4.000 \( A_{1} \) 2
\(\operatorname{G}_{2}(2)\) 4 19.234 \( G_{2} \) 2
\(\operatorname{SU}(2)_{3}\) 4 7.236 \( A_{1} \) 3
\(\operatorname{E}_{8}(3)\) 5 34.646 \( E_{8} \) 3
\(\operatorname{F}_{4}(2)\) 5 34.646 \( F_{4} \) 2
\(\operatorname{SU}(2)_{4}\) 5 12.000 \( A_{1} \) 4
\(\operatorname{E}_{7}(2)\) 6 14.472 \( E_{7} \) 2
\(\operatorname{G}_{2}(3)\) 6 100.617 \( G_{2} \) 3
\(\operatorname{SO}(5)_{2}\) 6 20.000 \( B_{2} \) 2
\(\operatorname{Sp}(4)_{2}\) 6 20.000 \( C_{2} \) 2
\(\operatorname{SU}(2)_{5}\) 6 18.592 \( A_{1} \) 5
\(\operatorname{SU}(3)_{2}\) 6 10.854 \( A_{2} \) 2
\(\operatorname{SO}(7)_{2}\) 7 28.000 \( B_{3} \) 2
\(\operatorname{SU}(2)_{6}\) 7 27.314 \( A_{1} \) 6
\(\operatorname{SO}(9)_{2}\) 8 36.000 \( B_{4} \) 2
\(\operatorname{SU}(2)_{7}\) 8 38.469 \( A_{1} \) 7
\(\operatorname{E}_{6}(2)\) 9 27.888 \( E_{6} \) 2
\(\operatorname{F}_{4}(3)\) 9 475.151 \( F_{4} \) 3
\(\operatorname{G}_{2}(4)\) 9 475.151 \( G_{2} \) 4
\(\operatorname{SO}(11)_{2}\) 9 44.000 \( B_{5} \) 2
\(\operatorname{SU}(2)_{8}\) 9 52.361 \( A_{1} \) 8
\(\operatorname{E}_{8}(4)\) 10 499.210 \( E_{8} \) 4
\(\operatorname{SO}(13)_{2}\) 10 52.000 \( B_{6} \) 2
\(\operatorname{SO}(5)_{3}\) 10 89.569 \( B_{2} \) 3
\(\operatorname{SO}(6)_{2}\) 10 24.000 \( D_{3} \) 2
\(\operatorname{Sp}(4)_{3}\) 10 89.569 \( C_{2} \) 3
\(\operatorname{Sp}(6)_{2}\) 10 89.569 \( C_{3} \) 2
\(\operatorname{SU}(2)_{9}\) 10 69.293 \( A_{1} \) 9
\(\operatorname{SU}(3)_{3}\) 10 36.000 \( A_{2} \) 3
\(\operatorname{SO}(15)_{2}\) 11 60.000 \( B_{7} \) 2
\(\operatorname{SO}(8)_{2}\) 11 32.000 \( D_{4} \) 2
\(\operatorname{SU}(2)_{10}\) 11 89.569 \( A_{1} \) 10
\(\operatorname{E}_{7}(3)\) 12 201.234 \( E_{7} \) 3
\(\operatorname{G}_{2}(5)\) 12 1996.556 \( G_{2} \) 5
\(\operatorname{SO}(10)_{2}\) 12 40.000 \( D_{5} \) 2
\(\operatorname{SO}(17)_{2}\) 12 68.000 \( B_{8} \) 2
\(\operatorname{SU}(2)_{11}\) 12 113.494 \( A_{1} \) 11
\(\operatorname{SO}(12)_{2}\) 13 48.000 \( D_{6} \) 2
\(\operatorname{SO}(19)_{2}\) 13 76.000 \( B_{9} \) 2
\(\operatorname{SO}(7)_{3}\) 13 210.193 \( B_{3} \) 3
\(\operatorname{SU}(2)_{12}\) 13 141.370 \( A_{1} \) 12
\(\operatorname{SO}(14)_{2}\) 14 56.000 \( D_{7} \) 2
\(\operatorname{SO}(21)_{2}\) 14 84.000 \( B_{10} \) 2
\(\operatorname{SU}(2)_{13}\) 14 173.502 \( A_{1} \) 13
\(\operatorname{SO}(5)_{4}\) 15 345.655 \( B_{2} \) 4
\(\operatorname{Sp}(4)_{4}\) 15 345.655 \( C_{2} \) 4
\(\operatorname{Sp}(8)_{2}\) 15 345.655 \( C_{4} \) 2
\(\operatorname{SU}(2)_{14}\) 15 210.193 \( A_{1} \) 14
\(\operatorname{SU}(3)_{4}\) 15 106.027 \( A_{2} \) 4
\(\operatorname{F}_{4}(4)\) 16 7402.794 \( F_{4} \) 4
\(\operatorname{G}_{2}(6)\) 16 7505.993 \( G_{2} \) 6
\(\operatorname{SO}(9)_{3}\) 16 408.635 \( B_{4} \) 3
\(\operatorname{SU}(2)_{15}\) 16 251.748 \( A_{1} \) 15
\(\operatorname{SU}(2)_{16}\) 17 298.471 \( A_{1} \) 16
\(\operatorname{SU}(2)_{17}\) 18 350.665 \( A_{1} \) 17
\(\operatorname{SU}(2)_{18}\) 19 408.635 \( A_{1} \) 18
\(\operatorname{E}_{6}(3)\) 20 426.246 \( E_{6} \) 3
\(\operatorname{G}_{2}(7)\) 20 25520.068 \( G_{2} \) 7
\(\operatorname{SO}(6)_{3}\) 20 141.370 \( D_{3} \) 3
\(\operatorname{Sp}(6)_{3}\) 20 1074.957 \( C_{3} \) 3
\(\operatorname{SU}(2)_{19}\) 20 472.683 \( A_{1} \) 19
\(\operatorname{SO}(5)_{5}\) 21 1162.522 \( B_{2} \) 5
\(\operatorname{Sp}(10)_{2}\) 21 1162.522 \( C_{5} \) 2
\(\operatorname{Sp}(4)_{5}\) 21 1162.522 \( C_{2} \) 5
\(\operatorname{SU}(2)_{20}\) 21 543.116 \( A_{1} \) 20
\(\operatorname{SU}(3)_{5}\) 21 279.765 \( A_{2} \) 5
\(\operatorname{SO}(7)_{4}\) 22 1479.852 \( B_{3} \) 4
\(\operatorname{SU}(2)_{21}\) 22 620.235 \( A_{1} \) 21
\(\operatorname{SU}(2)_{22}\) 23 704.346 \( A_{1} \) 22
\(\operatorname{SO}(8)_{3}\) 24 298.471 \( D_{4} \) 3
\(\operatorname{SU}(2)_{23}\) 24 795.752 \( A_{1} \) 23
\(\operatorname{E}_{7}(4)\) 25 4106.762 \( E_{7} \) 4
\(\operatorname{F}_{4}(5)\) 25 117593.688 \( F_{4} \) 5
\(\operatorname{G}_{2}(8)\) 25 79365.073 \( G_{2} \) 8
\(\operatorname{SU}(2)_{24}\) 25 894.757 \( A_{1} \) 24
\(\operatorname{SU}(2)_{25}\) 26 1001.665 \( A_{1} \) 25
\(\operatorname{SU}(2)_{26}\) 27 1116.780 \( A_{1} \) 26
\(\operatorname{SO}(10)_{3}\) 28 543.116 \( D_{5} \) 3
\(\operatorname{SO}(5)_{6}\) 28 3473.651 \( B_{2} \) 6
\(\operatorname{Sp}(12)_{2}\) 28 3473.651 \( C_{6} \) 2
\(\operatorname{Sp}(4)_{6}\) 28 3473.651 \( C_{2} \) 6
\(\operatorname{SU}(2)_{27}\) 28 1240.406 \( A_{1} \) 27
\(\operatorname{SU}(3)_{6}\) 28 671.560 \( A_{2} \) 6
\(\operatorname{SU}(2)_{28}\) 29 1372.847 \( A_{1} \) 28
\(\operatorname{G}_{2}(9)\) 30 228134.999 \( G_{2} \) 9
\(\operatorname{SO}(9)_{4}\) 30 4801.503 \( B_{4} \) 4
\(\operatorname{SU}(2)_{29}\) 30 1514.407 \( A_{1} \) 29
\(\operatorname{SU}(2)_{30}\) 31 1665.390 \( A_{1} \) 30
\(\operatorname{SO}(12)_{3}\) 32 894.757 \( D_{6} \) 3
\(\operatorname{SU}(2)_{31}\) 32 1826.100 \( A_{1} \) 31
\(\operatorname{SU}(2)_{32}\) 33 1996.840 \( A_{1} \) 32
\(\operatorname{SO}(7)_{5}\) 34 9389.869 \( B_{3} \) 5
\(\operatorname{SU}(2)_{33}\) 34 2177.916 \( A_{1} \) 33
\(\operatorname{SO}(6)_{4}\) 35 746.039 \( D_{3} \) 4
\(\operatorname{Sp}(6)_{4}\) 35 11045.289 \( C_{3} \) 4
\(\operatorname{Sp}(8)_{3}\) 35 11045.289 \( C_{4} \) 3
\(\operatorname{SU}(2)_{34}\) 35 2369.630 \( A_{1} \) 34
\(\operatorname{SO}(14)_{3}\) 36 1372.847 \( D_{7} \) 3
\(\operatorname{SO}(5)_{7}\) 36 9389.869 \( B_{2} \) 7
\(\operatorname{Sp}(4)_{7}\) 36 9389.869 \( C_{2} \) 7
\(\operatorname{SU}(2)_{35}\) 36 2572.287 \( A_{1} \) 35
\(\operatorname{SU}(3)_{7}\) 36 1487.902 \( A_{2} \) 7
\(\operatorname{SU}(2)_{36}\) 37 2786.190 \( A_{1} \) 36
\(\operatorname{SU}(2)_{37}\) 38 3011.644 \( A_{1} \) 37
\(\operatorname{F}_{4}(6)\) 39 1803237.970 \( F_{4} \) 6
\(\operatorname{SU}(2)_{38}\) 39 3248.953 \( A_{1} \) 38